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Does anyone know if persistent homology with integer coefficients are being used anywhere?

From what I understand, Carlsson's persistent module theory (http://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.116.2471&rep=rep1&type=pdf) works well for field coefficients (only).

Quote: "The correspondence established by Theorem 3.1 suggests the non-existence of simple classifications of persistence modules over a ground ring that is not a field." (pg 7 of the paper)

Thanks for any help.

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  • $\begingroup$ What is the relevance of this theorem for your purposes? $\endgroup$
    – Peter Saveliev
    Jul 23, 2018 at 2:34
  • $\begingroup$ @PeterSaveliev No specific purpose at the moment, just curious about what happens for non-fields. $\endgroup$
    – yoyostein
    Jul 24, 2018 at 16:43

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There is a paper "Defining and computing persistent Z-homology in the general case" by Romero et al., arxiv:1403.7086.

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  • $\begingroup$ Thanks for the reference. $\endgroup$
    – yoyostein
    Aug 3, 2017 at 2:13

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